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Question Number 197274 Answers: 0 Comments: 1

Question Number 197272 Answers: 2 Comments: 0

How to calculate this integral ∫^( (π/2)) _( 0) ((ln(1+sint))/(sint))dt

$$\mathrm{How}\:\mathrm{to}\:\mathrm{calculate}\:\mathrm{this}\:\mathrm{integral} \\ $$$$\underset{\:\mathrm{0}} {\int}^{\:\frac{\pi}{\mathrm{2}}} \:\frac{\mathrm{ln}\left(\mathrm{1}+{sint}\right)}{{sint}}{dt} \\ $$

Question Number 198332 Answers: 0 Comments: 1

Of men that attended a party, 30 of them wore coats, 20 wore ties and 10 wore hats. There were 4 men who wore coats and tie, or tie and hat or coat and hat. 14 men wore tie only with no coat and hat. Find the number of men who wore: a) coat, tie and hat b) hat only with no coat and hat.

$${Of}\:{men}\:{that}\:{attended}\:{a}\:{party},\:\mathrm{30}\:{of} \\ $$$${them}\:{wore}\:{coats},\:\mathrm{20}\:{wore}\:{ties}\:{and}\:\mathrm{10} \\ $$$${wore}\:{hats}.\:{There}\:{were}\:\mathrm{4}\:{men}\:{who}\:{wore} \\ $$$${coats}\:{and}\:{tie},\:{or}\:{tie}\:{and}\:{hat}\:{or}\:{coat}\:{and} \\ $$$${hat}.\:\mathrm{14}\:{men}\:{wore}\:{tie}\:{only}\:{with}\:{no} \\ $$$${coat}\:{and}\:{hat}.\:{Find}\:{the}\:{number}\:{of}\:{men} \\ $$$${who}\:{wore}: \\ $$$$\left.{a}\right)\:{coat},\:{tie}\:{and}\:{hat} \\ $$$$\left.{b}\right)\:{hat}\:{only}\:{with}\:{no}\:{coat}\:{and}\:{hat}. \\ $$

Question Number 198288 Answers: 1 Comments: 0

Question Number 197255 Answers: 0 Comments: 0

log 2=a log 3=b log 72=?

$$\mathrm{log}\:\mathrm{2}={a} \\ $$$$\mathrm{log}\:\mathrm{3}={b} \\ $$$$\mathrm{log}\:\mathrm{72}=? \\ $$

Question Number 197254 Answers: 0 Comments: 0

(((log_2 20)^2 −(log_2 5)^2 )/(log_2 10 ))=?

$$\frac{\left(\mathrm{lo}\underset{\mathrm{2}} {\mathrm{g}20}\right)^{\mathrm{2}} \:−\left(\mathrm{lo}\underset{\mathrm{2}} {\mathrm{g}5}\right)^{\mathrm{2}} \:}{\mathrm{lo}\underset{\mathrm{2}} {\mathrm{g}10}\:}=? \\ $$

Question Number 197253 Answers: 0 Comments: 0

log_3 12=a log _3 18=?

$$\mathrm{lo}\underset{\mathrm{3}} {\mathrm{g}12}={a} \\ $$$$\mathrm{log}\underset{\mathrm{3}} {\:}\mathrm{18}=?\: \\ $$

Question Number 197252 Answers: 0 Comments: 0

log_a x=30 log_b x=70 log_(ab) x=?

$$\mathrm{lo}\underset{{a}} {\mathrm{g}}{x}=\mathrm{30} \\ $$$$\mathrm{lo}\underset{{b}} {\mathrm{g}}{x}=\mathrm{70} \\ $$$$\mathrm{lo}\underset{{ab}} {\mathrm{g}}{x}=?\:\:\: \\ $$

Question Number 197251 Answers: 1 Comments: 0

log 2=0.30103 log 125=?

$$\mathrm{log}\:\mathrm{2}=\mathrm{0}.\mathrm{30103} \\ $$$$\mathrm{log}\:\mathrm{125}=? \\ $$

Question Number 197250 Answers: 0 Comments: 0

log 3=a log 4=b log_5 36=?

$$\mathrm{log}\:\mathrm{3}={a} \\ $$$$\mathrm{log}\:\mathrm{4}={b} \\ $$$$\mathrm{lo}\underset{\mathrm{5}} {\mathrm{g}36}=?\: \\ $$

Question Number 197249 Answers: 3 Comments: 0

log_6 2=a log_6 9=?

$$\mathrm{lo}\underset{\mathrm{6}} {\mathrm{g}2}={a} \\ $$$$\mathrm{lo}\underset{\mathrm{6}} {\mathrm{g}9}=?\:\: \\ $$

Question Number 197248 Answers: 0 Comments: 3

a,b,c∈R ((a + 2b − 3ac)/(3ac)) = ((a + 4b − bc)/b) Find: ((2b)/a) − ((3a)/b)

$$\mathrm{a},\mathrm{b},\mathrm{c}\in\mathbb{R} \\ $$$$\frac{\mathrm{a}\:+\:\mathrm{2b}\:−\:\mathrm{3ac}}{\mathrm{3ac}}\:\:=\:\:\frac{\mathrm{a}\:+\:\mathrm{4b}\:−\:\mathrm{bc}}{\mathrm{b}} \\ $$$$\mathrm{Find}:\:\:\:\frac{\mathrm{2b}}{\mathrm{a}}\:−\:\frac{\mathrm{3a}}{\mathrm{b}} \\ $$

Question Number 197247 Answers: 1 Comments: 0

calcul ∫^( +∞) _( 0) ((ln(cht))/(sh(t)))dt

$$\mathrm{calcul}\:\underset{\:\mathrm{0}} {\int}^{\:+\infty} \frac{{ln}\left({cht}\right)}{{sh}\left({t}\right)}{dt} \\ $$

Question Number 197245 Answers: 0 Comments: 1

Question Number 197242 Answers: 0 Comments: 0

Question Number 197241 Answers: 0 Comments: 0

Question Number 197239 Answers: 1 Comments: 0

Question Number 197238 Answers: 0 Comments: 1

Question Number 197234 Answers: 1 Comments: 0

Question Number 197229 Answers: 2 Comments: 1

Question Number 197228 Answers: 1 Comments: 0

Question Number 197227 Answers: 0 Comments: 0

Question Number 197226 Answers: 1 Comments: 0

Question Number 197225 Answers: 1 Comments: 0

Question Number 197212 Answers: 0 Comments: 1

Is ∫f(x)dx=∫_0 ^x lim_(x→t) f(x)dt?

$$\mathrm{Is}\:\int{f}\left({x}\right){dx}=\int_{\mathrm{0}} ^{{x}} \underset{{x}\rightarrow{t}} {\mathrm{lim}}{f}\left({x}\right){dt}? \\ $$

Question Number 197196 Answers: 1 Comments: 0

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